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fix fdtd pmls

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integrate them into the update operations
master
Jan Petykiewicz 3 years ago
parent 01b4971388
commit c0bbc1f46d
3 changed files with 174 additions and 62 deletions
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23
meanas/fdmath/functional.py
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@ -3,7 +3,8 @@ Math functions for finite difference simulations
Basic discrete calculus etc.
"""
from typing import Sequence, Tuple, Optional
from typing import Sequence, Tuple, Optional, Callable
import numpy # type: ignore
from .types import fdfield_t, fdfield_updater_t
@ -109,3 +110,23 @@ def curl_back(dx_h: Optional[Sequence[numpy.ndarray]] = None) -> fdfield_updater
return ch_fun
def curl_forward_parts(dx_e: Optional[Sequence[numpy.ndarray]] = None) -> Callable:
Dx, Dy, Dz = deriv_forward(dx_e)
def mkparts_fwd(e: fdfield_t) -> Tuple[Tuple[fdfield_t, ...]]:
return ((-Dz(e[1]), Dy(e[2])),
( Dz(e[0]), -Dx(e[2])),
(-Dy(e[0]), Dx(e[1])))
return mkparts_fwd
def curl_back_parts(dx_h: Optional[Sequence[numpy.ndarray]] = None) -> Callable:
Dx, Dy, Dz = deriv_back(dx_e)
def mkparts_back(h: fdfield_t) -> Tuple[Tuple[fdfield_t, ...]]:
return ((-Dz(h[1]), Dy(h[2])),
( Dz(h[0]), -Dx(h[2])),
(-Dy(h[0]), Dx(h[1])))
return mkparts_back

2
meanas/fdtd/__init__.py
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@ -160,7 +160,7 @@ Boundary conditions
"""
from .base import maxwell_e, maxwell_h
from .pml import cpml
from .pml import cpml_params, updates_with_cpml
from .energy import (poynting, poynting_divergence, energy_hstep, energy_estep,
delta_energy_h2e, delta_energy_j)
from .boundaries import conducting_boundary

211
meanas/fdtd/pml.py
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@ -7,31 +7,31 @@ PML implementations
"""
# TODO retest pmls!
from typing import List, Callable, Tuple, Dict, Any
from typing import List, Callable, Tuple, Dict, Sequence, Any, Optional
import numpy # type: ignore
from ..fdmath import fdfield_t
from ..fdmath import fdfield_t, dx_lists_t
from ..fdmath.functional import deriv_forward, deriv_back
__author__ = 'Jan Petykiewicz'
def cpml(direction: int,
polarity: int,
dt: float,
epsilon: fdfield_t,
thickness: int = 8,
ln_R_per_layer: float = -1.6,
epsilon_eff: float = 1,
mu_eff: float = 1,
m: float = 3.5,
ma: float = 1,
cfs_alpha: float = 0,
dtype: numpy.dtype = numpy.float32,
) -> Tuple[Callable, Callable, Dict[str, fdfield_t]]:
def cpml_params(
axis: int,
polarity: int,
dt: float,
thickness: int = 8,
ln_R_per_layer: float = -1.6,
epsilon_eff: float = 1,
mu_eff: float = 1,
m: float = 3.5,
ma: float = 1,
cfs_alpha: float = 0,
) -> Dict[str, Any]:
if direction not in range(3):
raise Exception('Invalid direction: {}'.format(direction))
if axis not in range(3):
raise Exception('Invalid axis: {}'.format(axis))
if polarity not in (-1, 1):
raise Exception('Invalid polarity: {}'.format(polarity))
@ -45,10 +45,8 @@ def cpml(direction: int,
sigma_max = -ln_R_per_layer / 2 * (m + 1)
kappa_max = numpy.sqrt(epsilon_eff * mu_eff)
alpha_max = cfs_alpha
transverse = numpy.delete(range(3), direction)
u, v = transverse
xe = numpy.arange(1, thickness + 1, dtype=float)
xe = numpy.arange(1, thickness + 1, dtype=float) # TODO: pass in dtype?
xh = numpy.arange(1, thickness + 1, dtype=float)
if polarity > 0:
xe -= 0.5
@ -59,8 +57,8 @@ def cpml(direction: int,
else:
raise Exception('Bad polarity!')
expand_slice_l: List[Any] = [None] * 3
expand_slice_l[direction] = slice(None)
expand_slice_l: List[Any] = [None, None, None]
expand_slice_l[axis] = slice(None)
expand_slice = tuple(expand_slice_l)
def par(x: numpy.ndarray) -> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]:
@ -76,52 +74,145 @@ def cpml(direction: int,
p0e, p1e, p2e = par(xe)
p0h, p1h, p2h = par(xh)
region_list = [slice(None)] * 3
region_list = [slice(None), slice(None), slice(None)]
if polarity < 0:
region_list[direction] = slice(None, thickness)
region_list[axis] = slice(None, thickness)
elif polarity > 0:
region_list[direction] = slice(-thickness, None)
region_list[axis] = slice(-thickness, None)
else:
raise Exception('Bad polarity!')
region = tuple(region_list)
se = 1 if direction == 1 else -1
return {
'param_e': (p0e, p1e, p2e),
'param_h': (p0h, p1h, p2h),
'region': region,
}
# TODO check if epsilon is uniform in pml region?
shape = list(epsilon[0].shape)
shape[direction] = thickness
psi_e = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
psi_h = [numpy.zeros(shape, dtype=dtype), numpy.zeros(shape, dtype=dtype)]
fields = {
'psi_e_u': psi_e[0],
'psi_e_v': psi_e[1],
'psi_h_u': psi_h[0],
'psi_h_v': psi_h[1],
}
def updates_with_cpml(
cpml_params: Sequence[Sequence[Optional[Dict[str, Any]]]],
dt: float,
dxes: dx_lists_t,
epsilon: fdfield_t,
*,
dtype: numpy.dtype = numpy.float32,
) -> Tuple[Callable[[fdfield_t, fdfield_t], None],
Callable[[fdfield_t, fdfield_t], None]]:
# Note that this is kinda slow -- would be faster to reuse dHv*p2h for the original
# H update, but then you have multiple arrays and a monolithic (field + pml) update operation
def pml_e(e: fdfield_t, h: fdfield_t, epsilon: fdfield_t) -> Tuple[fdfield_t, fdfield_t]:
dHv = h[v][region] - numpy.roll(h[v], 1, axis=direction)[region]
dHu = h[u][region] - numpy.roll(h[u], 1, axis=direction)[region]
psi_e[0] *= p0e
psi_e[0] += p1e * dHv * p2e
psi_e[1] *= p0e
psi_e[1] += p1e * dHu * p2e
e[u][region] += se * dt / epsilon[u][region] * (psi_e[0] + (p2e - 1) * dHv)
e[v][region] -= se * dt / epsilon[v][region] * (psi_e[1] + (p2e - 1) * dHu)
return e, h
Dfx, Dfy, Dfz = deriv_forward(dxes[1])
Dbx, Dby, Dbz = deriv_back(dxes[1])
def pml_h(e: fdfield_t, h: fdfield_t) -> Tuple[fdfield_t, fdfield_t]:
dEv = (numpy.roll(e[v], -1, axis=direction)[region] - e[v][region])
dEu = (numpy.roll(e[u], -1, axis=direction)[region] - e[u][region])
psi_h[0] *= p0h
psi_h[0] += p1h * dEv * p2h
psi_h[1] *= p0h
psi_h[1] += p1h * dEu * p2h
h[u][region] -= se * dt * (psi_h[0] + (p2h - 1) * dEv)
h[v][region] += se * dt * (psi_h[1] + (p2h - 1) * dEu)
return e, h
psi_E = [[None, None], [None, None], [None, None]]
psi_H = [[None, None], [None, None], [None, None]]
params_E = [[None, None], [None, None], [None, None]]
params_H = [[None, None], [None, None], [None, None]]
return pml_e, pml_h, fields
for axis in range(3):
for pp, polarity in enumerate((-1, 1)):
if cpml_params[axis][pp] is None:
psi_E[axis][pp] = (None, None)
psi_H[axis][pp] = (None, None)
continue
cpml_param = cpml_params[axis][pp]
region = cpml_param['region']
region_shape = epsilon[0][region].shape
psi_E[axis][pp] = (numpy.zeros(region_shape, dtype=dtype),
numpy.zeros(region_shape, dtype=dtype))
psi_H[axis][pp] = (numpy.zeros(region_shape, dtype=dtype),
numpy.zeros(region_shape, dtype=dtype))
params_E[axis][pp] = cpml_param['param_e'] + (region,)
params_H[axis][pp] = cpml_param['param_h'] + (region,)
pE = numpy.empty_like(epsilon, dtype=dtype)
pH = numpy.empty_like(epsilon, dtype=dtype)
def update_E(e: fdfield_t, h: fdfield_t, epsilon: fdfield_t) -> None:
dyHx = Dby(h[0])
dzHx = Dbz(h[0])
dxHy = Dbx(h[1])
dzHy = Dbz(h[1])
dxHz = Dbx(h[2])
dyHz = Dby(h[2])
dH = ((dxHy, dxHz),
(dyHx, dyHz),
(dzHx, dzHy))
pE.fill(0)
for axis in range(3):
se = (-1, 1, -1)[axis]
transverse = numpy.delete(range(3), axis)
u, v = transverse
dHu, dHv = dH[axis]
for pp in range(2):
psi_Eu, psi_Ev = psi_E[axis][pp]
if psi_Eu is None:
# No pml in this direction
continue
p0e, p1e, p2e, region = params_E[axis][pp]
dHu[region] *= p2e
dHv[region] *= p2e
psi_Eu *= p0e
psi_Ev *= p0e
psi_Eu += p1e * dHv[region] # note reversed u,v mapping
psi_Ev += p1e * dHu[region]
pE[u][region] += +se * psi_Eu
pE[v][region] += -se * psi_Ev
e[0] += dt / epsilon[0] * (dyHz - dzHy + pE[0])
e[1] += dt / epsilon[1] * (dzHx - dxHz + pE[1])
e[2] += dt / epsilon[2] * (dxHy - dyHx + pE[2])
def update_H(e: fdfield_t, h: fdfield_t, mu: fdfield_t = (1, 1, 1)) -> None:
dyEx = Dfy(e[0])
dzEx = Dfz(e[0])
dxEy = Dfx(e[1])
dzEy = Dfz(e[1])
dxEz = Dfx(e[2])
dyEz = Dfy(e[2])
dE = ((dxEy, dxEz),
(dyEx, dyEz),
(dzEx, dzEy))
pH.fill(0)
for axis in range(3):
se = (-1, 1, -1)[axis]
transverse = numpy.delete(range(3), axis)
u, v = transverse
dEu, dEv = dE[axis]
for pp in range(2):
psi_Hu, psi_Hv = psi_H[axis][pp]
if psi_Hu is None:
# No pml here
continue
p0h, p1h, p2h, region = params_H[axis][pp]
dEu[region] *= p2h # modifies d_E_
dEv[region] *= p2h
psi_Hu *= p0h
psi_Hv *= p0h
psi_Hu += p1h * dEv[region] # note reversed u,v mapping
psi_Hv += p1h * dEu[region]
pH[u][region] += +se * psi_Hu
pH[v][region] += -se * psi_Hv
h[0] -= dt / mu[0] * (dyEz - dzEy + pH[0])
h[1] -= dt / mu[1] * (dzEx - dxEz + pH[1])
h[2] -= dt / mu[2] * (dxEy - dyEx + pH[2])
return update_E, update_H

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